Hello, Michel,
Thank you for this interesting essay. As you will see from mine, you are one of the people I critique as overweighting geometry at the expense of energy. The logic of Grothendieck, in my humble opinion, is not the dynamic logic of the universe. I hope we may communicate on this point.
Best regards,
Joseph
Dear Joseph,
First thank you for looking at my essay. I will discuss yours next week and will try to give you extensive comments. My geometrical view is not faith, it follows from the properties of (multiple) qubit observables. In the essay, I found that these (projective) geometries can, in many cases, be described from the action of Grothendieck's dessins d'enfants. The latter probably have deep physical meaning I am currently trying to establish. Of course, one can have other views about the nature of the universe and try to justify them. In Lewis Caroll tale, as well as in Poincaré's "Science and Hypothesis", it is a matter of conventions.
Best regards,
Michel
Dear Dr. Michel,
Your essay is highly original and intriguing but at the same time it appears as if it is written for the experts in the field but not keeping general audience in the perspective. It is interesting to know how far the different geometric methods, you have followed in this article, are capable of solving other problems prevailing in QM. I congratulate you for producing such an innovative essay.
Sreenath
Dear Dr. Michel,
I appreciate your kind comments. It is good to learn that we share some common basic views regarding the existence of knowledge.
Best regards,
Sreenath
Dear Michal,
Thank you once again for the questions you asked me on my essay. If you visit the FQXi page ,( at the beginning of the page)
http://fqxi.org/community/essay
.............................................
I. GOALS & INTENT
The goals of the Foundational Questions Institute's Essay Contest (the "Contest") are to:
^ Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology;
.............................................
They used a word 'innovative', that may mean they want more fundamental thinking and may not be a report on current research prepared for discovery channel viewers...
Best
=snp
Michal
nice essay and interesting ideas, even though I need more knowledge about your math, to understand the technical derivations. I like the one about CHSH.
Best wishes
Mauro
Dear Michel Planat,
Having read your very interesting paper twice, I concluded that you would probably have little interest in mine. But after reading your comment on Stewart Heinrich's essay expressing your interest in the concept of self-awareness and the miraculous efficiency of mathematics for mimicking physical problems, both of which I address in my essay, I decided to invite you to read it and comment. I think it has little connection to your essay yet you may find a new perspective on these two topics.
Thank you for participating in this contest and good luck in the contest.
Best regards,
Edwin Eugene Klingman
Michel,
If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.
Jim
Dear Dr. Michel Planat
Thanks and congratulations for your poetic qubits.
I am mere a learner of physics here who have huge interests to know the fundamentals in nature. I think that to resolve the issues like "quantum non-locality and contextuality' in your essay, why not we ask the nature in different ways? I invite you to read my submitted essay for a quite new approach of asking the nature.
With my regards
Dipak
Dear Kumar,
Thank you for reading my essay and inviting me to read yours.
Yes, I like to have some poetry and visualization when it is possible.
You tell us that each access to reality is digitized and I agree.
But it occurs in a different way in classical physics and quantum mechanics.
Myself I did measurements of the frequency of ultrasable clocks in the past; there I recovered the structure of rational numbers, you can easily google with the keyword "number theory and 1/f noise" and find my contributions. This is well in the spirit of what you are writing. Quantum physics is more seriously difficult in this respect in the sense that it undress in bits (the eigenvalues of qubit observables) and it is much more difficult to organize them. In addition the observer participates in the undressing as Wheeler explained.
Best wishes,
Michel
Dear Michel,
Thank you for reading my essay and commenting on it. I have had a chance to review the two papers you referenced there. The Riemann paper discusses the details of a specific partition function, which I find interesting as I base the applicability of the Born probability to my wave function model on the partition function. The other paper, on time perception is also interesting. I had not seen the Poincare discussion of the Continuum, and found that fascinating, as well as your connection. I am somewhat confused as to whether you are proposing the phase locking as the 'mechanism' of time perception or of the 'scaling' of time perception? I can understand how this could relate to scaling, but not perception as I understand it.
Thanks again for reading my essay. I hope it stimulates some ideas for you.
Best,
Edwin Eugene Klingman
Dear Michel,
thank you for stopping by to comment on my essay. I was very much intrigued by your work and remember it from last year. It appears your presentation is more technical this year. I wish your interesting work reserves recognition is deserves among the specialists.
Best of luck :)
Dear Dr. Michel,
I have rated your innovative essay with maximum honors and wish you best of luck in the essay contest.
Best regards,
Sreenath
Dear Dr. Planat,
Your highly technical treatise was most absorbing, though in many parts I had difficulty following it. I will therefore state my comments along the broadest lines.
My view is that even if the emergence of random outcomes can be explained and contextualized in a variety of ways, the nature of information remains unchanged: It still defines the Observer's 'patch of reality' at any given moment, and continues to do so throughout evolution.
Even if we could describe the quantum world in perfect mathematical language, we would still have only described some small part of our Cosmos perfectly; and we would still be involved in our distinctive human Cosmos ... one that displays a continuous correlation between Bit and It over the course of evolution.
The observer does not interact with the whole field of reality regardless of how probabilities emerge, or how context affects them. Mathematics is the projection of the human mind on to the Cosmos - it will always be this, and it will always be entirely composed of Bits, thus keeping the Bit-It conundrum relevant to any definition of the Cosmos.
Though it is doubtless critical to investigate quantum reality as thoroughly as you do, I think we must also ask: 'Why do Bits 'match' Its so consistently at every instant of evolution - whatever their mathematics?' It would be interesting if the mathematics could be applied to the larger context of the perpetual Correlation of Bit to It.
As you can probably tell, this is one of the strands of my essay - which I think you would find interesting for the reasons I've stated.
Once again, yours is a very serious work, one with consequences; I am eager to hear your feedback, and wish you all the best.
John
Dear John,
Thank you so much for taking the time to read my (too technical) essay and writing your long comment. It may be improved at a futher stage of the research.
I expect that the paradigm of the Riemann sphere rigidified at three points may ultimately be useful for understanding what you name " the perpetual correlation of bit to it" in some analogy with what Jean Piaget did for the child cognition with the paradigm of the real projective plane (that I also introduce at the end of my essay).
I already red your excellent essay and I will write separate comments for it.
My best regards,
Michel
Dear Michel,
I think it is always good when someone examines the connection between ostensibly unrelated fields, finds certain parallels and then explores these to guide further research.
I am impressed by the fact that your approach permitted automating the search for proofs of Bell's theorem and related mathematical objects. I wonder if the different versions are sufficiently different from each other that this may also translate into differences in the difficulty of experimental set up. It seems that it might be useful to have a catalog/library of the objects found by your approach publicly available (perhaps even sortable by certain parameters), if only because it seems natural to assume that some versions may suggest certain deeper insights more readily than others.
At the conclusion it was not clear to me if you think that the dessin d'enfant for the Mermin Pentagram definitely does not exist or if this is still subject to further research. If it does not exist, how would you characterize the qualitative difference in contextuality between the two-qubit and three qubit case in terms of standard quantum mechanics?
All the best,
Armin
Dear Armin,
Yes, all proofs on non-locality and contextuality arising from the generalized Pauli group may be reached systematically. You can look at my/our recent papers on this subject from ArXiv.
The step towards dessins d'enfant is new. My essay is the first account of the relationship of finite geometries (contextual or not) and dessins. A publicly available catalog and, even better, all clues to reproduce my findings, will be given in the next paper.
I have some hints about why the Mermin's pentagram cannot be reproduced in this form (but the related Desargues configuration can be reproduced) and that constitutes a basic difference between two and three qubits first stated by Mermin himself.
An important fact is that several distinct dessins with different invariants give rise to the same geometry (as the Fano plane, the Mermin square or others), that is the absolute Galois group Gal(\bar(Q)/Q) is not enough to understand what is going on. Physically, it may have tremendous consequences regarding the link between the measurement space (here the Riemann sphere rigidified at three points) and the observable space (the finite geometry of compatible measurements). This should be distinguishable in measurements.
Thank you for your very relevant comments.
Best wishes.
Michel
Hi Michel,
I had the same question as Armin regarding the Mermin pentagram so I will have to read your forthcoming works on this topic. If a dessin d'enfents does *not* exist for the Mermin pentagram, what, in your opinion, does this mean for contextuality and, more generally, the Kochen-Specker theorem?
Ian Durham
Dear Ian,
Excellent question left in abeyance in the paper, according to Belyi's theorem It means the lack on an algebraic curve associated to the pentagram. As there are 12096 three-qubit pentagrams it also means challenging questions for the whole finite geometry of operators.
Michel
Hi Michel,
Interesting. I'll have to think about that a bit.
Ian